I’ve never heard of remote start being used as a way to idle your car while doing other stuff. It’s most commonly used to defrost a car in the winter without having to get into it and sit in the freezing car while you’re not moving anyway.
There’s a time limit on it on my car, I think about 10 minutes or something pretty sane. If you don’t get into your car by then it turns back off automatically.
I once spent two cold nights standing on my head putting an aftermarket remote start system into an old BMW.
And sometimes I did use it to keep the car running while doing other stuff. This function was a design intent of the device.
It would work like this: Drive to a destination not so far away on a cold wintry day and put transmission in park like usual. Then, push the start button on the remote and turn the ignition switch off.
After that: Remove key, get out, lock doors, go do whatever quick errand it was that had us out to begin with, and return to a car that was finally actually warm inside. The engine and accessories would continue running uninterrupted, like nothing ever happened.
After returning: Put key in, turn it to "on", select a gear, on to the next destination. Engine stays running the whole time.
When I read about this function, I figured I'd never use it. But it did work very well and my then-wife liked it quite a lot. Also if short, cold runs are bad for things like bearing wear and oil contamination, then keeping it running and letting it get up to operating temperature was perhaps a nicer way to treat that old engine than the alternative of never letting it really get warm might have been.
(It would time out and turn off after about 10 or 15 minutes. Otherwise, the engine would cease immediately upon touching the brake pedal if the ignition switch wasn't on.)
There’s a time limit on it on my car, I think about 10 minutes or something pretty sane. If you don’t get into your car by then it turns back off automatically.